In 2.4, Olivia does not appear, but there is a conversation between Orsino and Viola where Orsino describes his love for Olivia and Viola covertly confesses her love for Orsino.

In this passage, we find out a few things about Orsino. One, he doesn't believe in taking no for an answer in matters of love and would pursue someone until he wore her down enough to accept his suit. And two, he doesn't believe a man can love as strongly as a woman:

ORSINO There is no woman’s sides Can bide the beating of so strong a passion As love doth give my heart. No woman’s heart So big, to hold so much. They lack retention. Alas, their love may be called appetite, No motion of the liver, but the palate, That suffer surfeit, cloyment, and revolt; But mine is all as hungry as the sea, And can digest as much. Make no compare Between that love a woman can bear me And that I owe Olivia.

In 3.1, Olivia's feelings for Cesario/Viola are revealed. It can be noted that it's important to her that the person she loves finds her honorable and that she thinks that pity is a step in the right direction for love, meaning that if C/V's heart is soft enough towards her to feel sorry for her, surely love could follow. Olivia would also rather her love be denied by someone she finds noble than someone she finds cruel:

OLIVIA Why then methinks ’tis time to smile again. O world, how apt the poor are to be proud! If one should be a prey, how much the better To fall before the lion than the wolf! (clock strikes) The clock upbraids me with the waste of time. Be not afraid, good youth, I will not have you. And yet when wit and youth is come to harvest, Your wife is like to reap a proper man. There lies your way, due west.